Compact Matrix Quantum Groups and Their Combinatorics

An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.

List of contents

Preface. Part I. Getting Started: 1. Introducing quantum groups; 2. Representation theory; Part II. Partitions Enter The Picture: 3. Partition quantum groups; 4. The representation theory of partition quantum groups; 5. Measurable and topological aspects; Part III. Further Examples And Applications: 6. A unitary excursion; 7. Further examples; 8. Back to the game; Appendix A; Appendix B; Appendix C.

About the author

Amaury Freslon is an expert in the theory of compact quantum groups with an international recognition. He earned his Ph.D. in Paris in 2013 and has since then written many scientific publications in the field. Dr. Freslon has taught the subject multiple times in several universities across Europe.

Product details

• Authors: Amaury Freslon, Amaury (Universite Paris-Saclay) Freslon
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 01.08.2023
• EAN: 9781009345736
• ISBN: 978-1-0-0934573-6
• No. of pages: 300
• Series: London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; Social sciences, law, business > Media, communication > Communication science; Algebra, MATHEMATICS / Algebra / General, Discrete Mathematics, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Combinatorics & graph theory, Calculus & mathematical analysis, Information theory, Mathematical foundations, Calculus and mathematical analysis, Combinatorics and graph theory